You should first try to address the reason for the files accumulating.
Most likely you are using a resident scanner that is preventing the files from being deleted. You should exclude the scratch directory from being protected by the scanner so that MailEnable itself can delete the files.

Alternatively, it is possible that if you are using an AV scanner that has issues with cleaning up/scanning. ClamAV can have this problem.

If you cannot address the issue based on above, then you may wish to schedule a script (via Control Panel) that stops the MTA, deletes the contents of the scratch dir, and the starts the mta.

The problem with ClamAV is not so much that you need to exclude the directory, but that the scanner itself has threading issues when being called concurrently. ie: It can have issues (like those your experiencing) when you attempt to run multiple instances of the scanner at the same time. The solution is typically to lower the number of transfer threads for the MTA to 1 or 2 threads. This should remove contention for the scanner and will you should notice that the hangover files should not appear. Unless you are running a large number of users or process a large number of messages, the reduction of the mta transfer thread should not cause delays.

Does the ClamWin Article at https://www.mailenable.com/kb/content/article.asp?ID=ME020484 apply to the ClamAv scanner that installs with MailEnable Enterprise 9.76? I ask because the product name in the article is ClamWin not ClamAV and it instructs you to download and install ClamWIN, but ClamAV installs with MailEnable.

Specifically we were wanting to know if clamdscan.exe can handle multiple MTA threads. We need an AV scanner that integrates seamlessly (plays nice) with Mail Enable but can also handle 24-32 MTA threads.

The ClamAV scanner included in version 6 on wards is not ClamWin (will update the article accordingly). Answering your question; if using the ClamAV out of box solution we provide then the MTA thread count can run at 64 threads and the clamdscan will handle this.